How to fill a mesh with solid color
You can create multiple materials for the object in the materials tab of the properties panel.  Then, on edit mode, use the assign buttons in the materials tab to give the selected faces the selected material.  By default all faces are assigned the first material you create.





Note: the rendering properties of a material can be found in the surface rollout.  But materials, by default, have a gray viewport color, this can be changed for each material at the bottom of the material's settings.